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A bar is creating a new signature drink. There are five possible alcoh
[#permalink]
01 Dec 2022, 06:38
01 Dec 2022, 06:38
Expert Reply
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Question Stats:
76% (01:05) correct
23% (03:06) wrong based on 17 sessions
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A bar is creating a new signature drink. There are five possible alcoholic ingredients in the drink: rum, vodka, gin, peach schnapps, or whiskey. There are five possible non-alcoholic ingredients: cranberry juice, orange juice, pineapple juice, limejuice, or lemon juice. If the bar uses two alcoholic ingredients and two non-alcoholic ingredients, how many different drinks are possible?
A. 100
B. 25
C. 50
D. 75
E. 3600
A. 100
B. 25
C. 50
D. 75
E. 3600
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Re: A bar is creating a new signature drink. There are five possible alcoh
[#permalink]
02 Dec 2022, 09:22
02 Dec 2022, 09:22
Expert Reply
Soln: The first step in this problem is to calculate the number of ways of selecting
two alcoholic and two non-alcoholic ingredients. Since order of arrangement does not
matter, this is a combination problem.
The number of combinations of n objects taken r at a time is
C(n,r) = n!/(r!(n-r!))
The number of combinations of alcoholic ingredients is
C(5,2) = 5!/(2!(3!))
C(5,2) = 120/(2(6))
C(5,2) = 10
The number of combinations of non-alcoholic ingredients is
C(5,2) = 5!/(2!(3!))
C(5,2) = 120/(2(6))
C(5,2) = 10
The number of ways these ingredients can be combined into a drink can be
determined by the Multiplication Principle. The Multiplication Principle tells us that the
number of ways independent events can occur together can be determined by
multiplying together the number of possible outcomes for each event.
The number of possible drinks is
= 10 * 10
= 100
two alcoholic and two non-alcoholic ingredients. Since order of arrangement does not
matter, this is a combination problem.
The number of combinations of n objects taken r at a time is
C(n,r) = n!/(r!(n-r!))
The number of combinations of alcoholic ingredients is
C(5,2) = 5!/(2!(3!))
C(5,2) = 120/(2(6))
C(5,2) = 10
The number of combinations of non-alcoholic ingredients is
C(5,2) = 5!/(2!(3!))
C(5,2) = 120/(2(6))
C(5,2) = 10
The number of ways these ingredients can be combined into a drink can be
determined by the Multiplication Principle. The Multiplication Principle tells us that the
number of ways independent events can occur together can be determined by
multiplying together the number of possible outcomes for each event.
The number of possible drinks is
= 10 * 10
= 100
gmatclubot
Re: A bar is creating a new signature drink. There are five possible alcoh [#permalink]
02 Dec 2022, 09:22
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